This increase in popularity for Android development really started to take off in 2015, but it was two years later, in 2017, when Kotlin really came to the fore. That was when Google officially announced support for Kotlin as a development language for Android.
When Android Studio 3.0 was released in October 2017, there was no longer a major technical obstacle to the adoption of Kotlin in established projects. Organizations or teams that had been concerned about pre-release versions of plugins or IDEs could now try Kotlin with stable tools and the full, long-term support of Google. This allowed many teams to adopt the language, and thus began the surge in Kotlin's popularity that we see today.
This community support for Kotlin came about largely because of Android's dependency on Java 7 and Java 8. While newer versions of Java have much more modern functionality, Android was stuck with Java 7 and 8 for long-term compatibility. This meant that developers didn't have access to more modern features, such as lambdas, without additional plugins or updating their target language, which wasn't always feasible.
The adoption of Kotlin provided a more modern-feeling language that was still bytecode-compatible with the JVM versions that Android required. As prominent members of the Android development community began speaking out in favor of Kotlin, more and more developers started to give it a try. With official support from Google, pitching Kotlin to a team became a much easier sell, and teams could begin experimenting with Kotlin with minimal risk.
All of this has resulted in Kotlin becoming a major part of the Android ecosystem today.